Annotated Bibliography of Resources for Educational Reform, Coherent Teaching Practice, and Improved Student Learning
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Lambert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29-63.
In popular culture and in classrooms, mathematics is associated with certainty, with knowing how to get the right answer. On the other hand, mathematicians make conjectures, examine assumptions, ask questions, explain their reasoning, and reflect on their thinking and that of others. Lambert questions whether it might be possible to produce lessons in which students exhibit the qualities of doing mathematics in the way that mathematicians do. In this article, she describes a research and development project designed to explore this question. She presents an episode of teaching and learning involving a lesson with fifth graders on exponents. The students are given a problem but no method to solve the problem. The problem is chosen for its potential to expose a wide range of students' thinking about mathematics. The level of discussion in the class was quite sophisticated as students considered possible solutions, challenged each other, and refined their thinking. The students were engaged in mathematical discourse. What did it take to get the students to do this? Lambert designed lessons that engaged students in authentic mathematical activity. She initiated and supported social interactions appropriate to making mathematical arguments in response to students' conjectures. This is in direct contrast to the conventional activities that characterize school mathematics.
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